0=-16t^2+90t+7

Solution for 0=-16t^2+90t+7 equation:

0=-16t^2+90t+7

We move all terms to the left:

0-(-16t^2+90t+7)=0

We add all the numbers together, and all the variables

-(-16t^2+90t+7)=0

We get rid of parentheses

16t^2-90t-7=0

a = 16; b = -90; c = -7;
Δ = b2-4ac
Δ = -902-4·16·(-7)
Δ = 8548
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8548}=\sqrt{4*2137}=\sqrt{4}*\sqrt{2137}=2\sqrt{2137}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2137}}{2*16}=\frac{90-2\sqrt{2137}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2137}}{2*16}=\frac{90+2\sqrt{2137}}{32}
$